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Seminar Thermodynamische Modellierung und Analyse von Phasenübergängen (Archiv)

zu den aktuellen Veranstaltungen

Dienstag, 22.11.2016, 13:00 Uhr (WIAS-406)
Martin Kraus, Ostbayerische Technische Hochschule Regensburg:
Modeling of porous metal-electrolyte interfaces
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Dienstag, 10.02.2015, 12:30 Uhr (WIAS-406)
Prof. Eckhard Spohr, Universität Duisburg-Essen:
MD Simulations of structure and reaction dynamics at the liquid / solid electrode interface
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Donnerstag, 23.10.2014, 10:00 Uhr (WIAS-406)
Jan-Frederik Pietschmann, Technische Universität Darmstadt, Department of Mathematics:
Motion and size exclusion - Derivation and properties of non-linear cross-diffusion models
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Modelling the transport of particles with size exclusion is of high relevance in many current applications, e.g., in molecular and cell biology. In the case of a single type of particle, various models have been proposed at the continuum level or derived from microscopic models typically leading to nonlinear drift-diffusion equations for the particle density. Less attention has been paid to the case of several different particles, which is, however, very relevant in many practical problems such as the transport of ions through narrow membrane channels. In this talk we will discuss the derivation of such a model based on a formal limit of a jump process and discuss several properties such as existence of solutions and long-time behaviour.

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WIAS Berlin
Dienstag, 17.12.2013, 10:00 Uhr (WIAS-406)
Dr. Dirk Peschka, WIAS Berlin:
Modelling and numerics of thin-films using variational principles
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Dienstag, 08.10.2013, 13:00 Uhr (WIAS-406)
Prof. Katharina Krischer, Technische Universität München:
Cooperative phenomena during electrochemical reactions
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Many electrochemical reactions exhibit self-organization phenomena such as oscillatory reaction rates, traveling reactivity waves which propagate on the electrode surface, or the partitioning of the electrode in domains with different properties. In the talk I will discuss a hierarchy of nonlinear phenomena observed during the electrooxidation of carbon monoxide, a prototypical electrocatalytic reaction, which is also of practical importance in the context of fuel cell catalysis. After introducing the experimental observations, I will focus on how the phenomena can be modeled with a mean-field approach, and I will discuss the mechanisms that lead to the different dynamic instabilities.

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WIAS Berlin
Dienstag, 24.09.2013, 12:30 Uhr (WIAS-406)
Anke Böttcher, Technische Universität Darmstadt:
The hybrid phase field model - Introduction and numerical examples
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Dienstag, 02.07.2013, 12:30 Uhr (WIAS-406)
Johannes Höwing, Universität Hamburg:
Stability of solitary waves in generalized KdV, Boussinesq, and Euler-Korteweg equations
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
We establish stability of solitary waves in generalized KdV and Boussinesq equations under the assumption that the nonlinearity $p$ satisfies $p”>0$ and $p”'leq0.$ In particular, the Boussinesq equation with $p(v)=kv^-gamma$ with $gammageq1,$ $k>0$ describes the flow of an inviscid isothermal ideal (barotropic) fluid with constant capillarity. Under the sole assumption that $p$ is strictly convex, we still can conclude stability of small-amplitude solitary waves in generalized Euler-Korteweg (EK) equations, such as the generalized Gross-Pitaevskii equation. In the EK equation we show instability of any standing solitary wave.
Lastly, time permitting, we will discuss a recent joint work with Heinrich Freistühler on stability of solitary waves in extended Boussinesq equations with quadratic-cubic nonlinearity which were recently proposed by Heimburg and Jackson as an alternative to the Hodgkin-Huxley and FitzHugh-Nagumo equations in the modeling of pulse propagation in nerves.
The proofs are basically an evaluation of the respective moment of instability (Grillakis, Shatah, Strauss 1987), a tool which detects unstable point spectrum of the linearized operator, and which is related to the Evans function.

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WIAS Berlin
Dienstag, 26.03.2013, 12:30 Uhr (WIAS-406)
Julian Tugaut, Universität Bielefeld:
Long-time convergence of a McKean-Vlasov diffusion
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
A McKean-Vlasov diffusion corresponds to the hydrodynamical limit of a particle in a mean-field system. Benachour, Roynette and Vallois proved the convergence in law of such a processus. Cattiaux, Guillin and Malrieu extended this result by adding an external force which corresponds to the gradient of a convex potential. Carrillo, McCann and Villani proved a similar result in a non-convex case by assuming a conservation of the center of mass. By using the free-energy functionnal and the results on the invariant probabilities, the long-time convergence will be proved under natural hypotheses concerning the initial law.

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WIAS Berlin
Dienstag, 22.01.2013, 12:30 Uhr (WIAS-406)
Dr. Pavel Gurevich/Dr. Sergey Tikhomirov, Freie Universität Berlin:
Reaction-diffusion equations with spatially distributed hysteresis
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
We consider continuous and discrete reaction-diffusion equations involving a hysteretic discontinuity in the source term, which is defined at each spatial point. In particular, such problems describe chemical reactions and biological processes in which diffusive and nondiffusive substances interact according to hysteresis law. As a result various spatial and spatio-temporal patterns may appear. We found a broad class of initial data (transverse functions) for which a solution exists, is unique, and continuously depends on initial data. As far as we know, this is the first well-posedness result for such systems with hysteresis. For the nontransverse case, we consider a spatial discretization of the problem and analyze emerging spatio-temporal patterns. Interestingly, for two-dimensional domains, those patterns depend on the grid structure.

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WIAS Berlin
Dienstag, 15.01.2013, 12:30 Uhr (WIAS-406)
Paul Gajewski, WIAS Berlin:
Analysis of a modified Nernst-Planck-Poisson system: Thermodynamic equilibrium
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Dienstag, 18.12.2012, 12:30 Uhr (WIAS-ESH)
Prof. Dr. Jürgen Sprekels, WIAS Berlin:
Mathematical modeling of hysteresis - Part III
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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WIAS Berlin
Dienstag, 11.12.2012, 12:30 Uhr (WIAS-ESH)
Prof. Dr. Jürgen Sprekels, WIAS Berlin:
Mathematical modeling of hysteresis - Part II
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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WIAS Berlin
Montag, 10.12.2012, 12:30 Uhr (WIAS-406)
Prof. Volker Schmidt, Universität Ulm:
Stochastic modeling of the 3D morphology of energy materials on various length scales
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Stochastic modeling of the 3D morphology of energy materials on various length scales Volker Schmidt and Ole Stenzel Ulm University, Institute of Stochastics The morphological 3D structure of complex porous or composite materials is closely related to their physical properties, in particular with transport processes of charges, gases, or fluids, and with degradation mechanisms occurring in these materials. Thus, the systematic development of ?designed? 3D morphologies with improved physical properties is an important problem which has various applications, e.g., in Li-ion batteries, organic solar cells, and fuel cells. Mathematical models from stochastic geometry can help to solve this problem, since they can be used to provide a parametric description of complex 3D morphologies in existing materials. Moreover, systematic modifications of model parameters and the combination of stochastic morphology models with numerical transport models offer the opportunity to construct new ?virtual? (but still realistic) 3D morphologies with improved physical properties, using model-based computer simulations. In this talk we present several types of models from stochastic geometry which have been developed for complex 3D morphologies of energy materials on various length scales. First, we discuss two different stochastic modeling approaches for the 3D microscale structure of electrodes in Li-ion batteries: a germ-grain model for the pore phase of uncompressed electrodes [1], and a graph-based model for the solid phase of compressed electrodes [2]. In both cases the models are fitted to experimental 3D data gained by synchrotron tomography. Then, we consider a germ-grain model for mesoscale morphologies of photoactive layers in organic solar cells [3] which has been fitted to 3D image data from electron tomography. It turns out that the quality of percolation pathways, considering the charge carrier mobility, and also the exciton quenching efficiency strongly depends on the mesoscale morphology [4]. Finally, we discuss a 3D network model on a molecular scale for charge transport simulations in large domains of amorphous organic semiconductors [5] and we show how the usage of segmentation methods can reduce computational costs of such simulations by several orders of magnitude [6]. Literature [1] R. Thiedmann, O. Stenzel, A. Spettl, P.R. Shearing, S.J. Harris, N.P. Brandon and V. Schmidt (2011) Stochastic simulation model for the 3D morphology of composite materials in Li-ion batteries. Computational Materials Science 50, 3365-3376. [2] O. Stenzel, D. Westhoff, I. Manke, M. Kasper, D.P. Kroese and V. Schmidt (2012) Graph-based simulated annealing: A hybrid approach to stochastic modeling of complex microstructures. Modeling and Simulation in Materials Science and Engineering (submitted) [3] O. Stenzel, H. Hassfeld, R. Thiedmann, L.J.A. Koster, S.D. Oosterhout, S.S. van Bavel, M.M. Wienk, J. Loos, R.A.J. Janssen and V. Schmidt (2011) Spatial modeling of the 3D morphology of hybrid polymer-ZnO solar cells, based on electron tomography data. Annals of Applied Statistics 5, 1920-1947. [4] O. Stenzel, L.J.A. Koster, R. Thiedmann, S.D. Oosterhout, R.A.J. Janssen and V. Schmidt (2012) A new approach to model-based simulation of disordered polymer blend solar cells. Advanced Functional Materials 22, 1236-1244. [5] B. Baumeier, O. Stenzel, C. Poelking, D. Andrienko and V. Schmidt (2012) Stochastic modeling of molecular charge transport networks. Physical Review B (submitted) [6] T.J. Brereton, O. Stenzel, B. Baumeier, D. Andrienko, V. Schmidt and D.P. Kroese (2012) Efficient simulation of Markov chains using segmentation. Methodology and Computing in Applied Probability (submitted)

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WIAS Berlin
Dienstag, 20.11.2012, 12:30 Uhr (WIAS-406)
Dr. Maren Hantke, Universität Magdeburg:
Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The mass transfer is modeled by a kinetic relation. We prove existence and uniqueness results. Further, we construct the exact solution for Riemann problems. We derive analogous results for the cases of initially one phase with resulting condensation by compression or evaporation by expansion. Further we present numerical results for these cases. We compare the results to similar problems without phase transition.

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WIAS Berlin
Dienstag, 13.11.2012, 12:30 Uhr (WIAS-ESH)
Prof. Dr. Jürgen Sprekels, WIAS Berlin:
Mathematical modeling of hysteresis
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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Seminar “Thermodynamische Modellierung und Analyse von Phasenübergängen”

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WIAS Berlin
Dienstag, 06.11.2012, 12:30 Uhr (WIAS-406)
Dr. Jan Giesselmann, WIAS Berlin:
Entropy dissipative schemes for compressible 2-phase flows
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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Seminar Thermodynamische Modellierung und Analyse von Phasenübergängen

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WIAS Berlin
Dienstag, 30.10.2012, 12:30 Uhr (WIAS-406)
Manuel Landstorfer, WIAS Berlin:
Ionic Liquids - Issues, challenges and recent theoretical descriptions
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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Seminar Thermodynamische Modellierung und Analyse von Phasenübergängen

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WIAS Berlin
Dienstag, 23.10.2012, 12:30 Uhr (WIAS-406)
Dr. Robert Huth, WIAS:
On a Fokker--Planck equation coupled with a constraint
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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Seminar Thermodynamische Modellierung und Analyse von Phasenübergängen

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WIAS Berlin
Dienstag, 16.10.2012, 12:30 Uhr (WIAS-406)
Clemens Guhlke, WIAS:
Sharp limit of the viscous Cahn-Hilliard equation in the context of the 2nd law of thermodynamics
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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Seminar Thermodynamische Modellierung und Analyse von Phasenübergängen

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WIAS Berlin
Dienstag, 09.10.2012, 12:30 Uhr (WIAS-406)
Prof. Hans Wilhelm Alt, Technische Universität München:
Free energy inequality in the limit of phase transitions
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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Seminar “Thermodynamische Modellierung und Analyse von Phasenübergängen”

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WIAS Berlin
Donnerstag, 13.09.2012, 10:30 Uhr (WIAS-406)
Prof. Robert Denk, Universität Konstanz:
Pseudodifferential operators and maximal $L^p$-regularity
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
In the analysis of evolution equations, pseudodifferential operators appear in a natural way, e.g., in connection with the reduction to the boundary method. One approach to prove well-posedness (local in time) of the nonlinear equation is to show maximal $L^p$-regularity for the linearized problem. In the talk we will discuss several classes of (vector-valued) pseudodifferential operators and maximal regularity results for them. Apart from pseudodifferential operators in the whole space or on a closed manifold, so-called singular Green operators appear in the theory of boundary value problems. For a suitably defined class of singular Green operators, maximal regularity can be shown using the concept of $mathcal R$-boundedness. As an application, we mention the Stokes equation in cylindrical domains.

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Seminar “Thermodynamische Modellierung und Analyse von Phasenübergängen”

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WIAS Berlin
Dienstag, 14.08.2012, 12:30 Uhr (WIAS-406)
Michael Helmers, Universität Bonn:
Convergence of a surface phase field model for axisymmetric two-phase biological membranes
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Shapes of bilayer membranes made of two lipid phases are governed by an energy that consists of an elastic part for each lipid phase and penalises phase boundaries. Diffuse interface approaches have been applied successfully to analyse such membranes, though many results are formal or rely on strong regularity assumptions. In the talk, we consider a surface phase field approximation of the spontaneous curvature model and study convergence to a sharp interface limit in a rotationally symmetric setting. Particular attention is paid to the regularity of limit membranes across lipid interfaces: exploring two different couplings between phase fields and elastic terms, we obtain either the classical model or an extension that assigns a "bending energy" also to possibly non-smooth connections.

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WIAS Berlin
Dienstag, 22.05.2012, 12:30 Uhr (WIAS-406)
Prof. Ansgar Jüngel, Technische Universität Wien:
Entropy structure of cross-diffusion models in biology and physics
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
Diffusive systems of nonlinear partial differential equations with cross-diffusion terms appear in many biological and physical applications like chemotaxis, tumor modeling, and gas dynamics. The main feature of these systems is that the diffusion matrix is generally neither symmetric nor positive definite, which makes the mathematical analysis very challenging. Interestingly, these systems possess an entropy structure, i.e., there exist so-called entropy variables which make the diffusion matrix symmetric and positive definite. The existence of these variables is equivalent to the existence of an entropy which turns out to be a Lyapunov functional and leads to a priori estimates. Although the maximum principle does not hold for such systems, the entropy variables naturally lead to lower or upper bounds of the solution. This structure is explained for three examples: a Keller-Segel model for chemotaxis with additional cross-diffusion; a tumor-growth model which describes tumor encapsulation; and the Maxwell-Stefan system for multicomponent gas mixtures. The existence of global weak solutions is proved and numerical examples are presented.

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WIAS Berlin
Dienstag, 08.05.2012, 12:30 Uhr (WIAS-406)
Matthias Köhne, Technische Universität Darmstadt, Center of Smart Interfaces:
On incompressible Newtonian flows - Artificial boundary conditions and free boundary problems
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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Seminar Thermodynamische Modellierung und Analyse von Phasenübergängen

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WIAS Berlin
Dienstag, 06.12.2011, 12:30 Uhr (WIAS-406)
Dr. Olaf Klein, WIAS:
Hysteresis operators for vector-valued inputs, their representation by functions on strings, and Madelung's rules
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
In Brokate-Sprekels 1996, an representation formula for hysteresis operators acting on scalar-valued continuous input functions being piecewise monotone has been presented. In the current work, hysteresis operators dealing with inputs in a general normed vector space are investigated, and a similar representation formula is derived. This formula is used to discus some aspects of a vectorial Formulation of the Madelung's rules.

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WIAS Berlin
Dienstag, 11.10.2011, 12:30 Uhr (WIAS-406)
Prof. Martin Brokate, Technische Universität München:
Optimal control of ODE systems involving a variational inequality
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Montag, 11.07.2011, 10:00 Uhr (WIAS-ESH)
Dr. Gabriele Witterstein, Technische Universität München:
Two-phase compressible fluids
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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WIAS Berlin
Dienstag, 28.06.2011, 12:30 Uhr (WIAS-406)
Oliver Lass/Tim Seger, Universität Konstanz:
Analysis and numerics for an elliptic parabolic system arising in the modeling of batteries and fuel cells
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Dienstag, 17.05.2011, 12:30 Uhr (WIAS-406)
Prof. Antonio Segatti, Università degli Studi di Pavia:
Some observation on an ultra fast diffusion equation with application to phase transition problems
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

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WIAS Berlin
Montag, 16.05.2011, 14:00 Uhr (WIAS-ESH)
PD Dr. Arnulf Latz, Fraunhofer ITWM, Kaiserslautern:
Thermodynamic consistent modeling and simulations of transport on micro and nanoscales in Li Ion batteries
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

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WIAS Berlin